Cryptography: The Mathematics of Secret Codes

密码学：密码的数学

• 批准号: 0099220
• 负责人: Janet Beissinger
• 金额: $ 39.81万
• 依托单位: University of Illinois at Chicago
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-09-01 至 2006-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0099220&HistoricalAwards=false
• 关键词: Cryptography; Mathematics; Secret; Codes

This project develops an 8-week middle-school mathematics module that introduces cryptography, the science of sending secret messages, while teaching and reinforcing the learning of related mathematical concepts. The topics range from the classical encryption systems and the historic context in which they were used through powerful modern encryption systems that provide secrecy in electronic messages today. The module also covers passwords and codes that correct errors in the transmission of information. Public awareness of the importance of cryptography is growing, as is the need to understand the issues involved. The study of cryptography provides an interesting context for students to apply traditional mathematical skills and concepts. Mathematical topics covered include percents, probability, functions, prime numbers, decimals, inverses and modular arithmetic. The main product is a middle-school student book, with accompanying teacher materials. A web site is being developed that supports the activities in this book. Abbreviated modules for Grades 3, 4 and 5 are also being developed, as well as an instructor's guide for adapting the materials for use in informal educational settings such as museums and after-school programs. The development of the module involves piloting and field-testing by experienced classroom teachers from diverse school communities and instructors of informal educational programs. Evaluation includes review by mathematicians and educators, as well as an investigation into the level of students' understanding of the topics studied.

该项目开发了一个为期8周的中学数学模块，该模块介绍了密码学，即发送秘密信息的科学，同时教导和加强了相关数学概念的学习。 主题范围从经典的加密系统以及通过强大的现代加密系统使用的历史背景，这些系统在当今的电子信息中提供了保密性。 该模块还涵盖了在信息传输中纠正错误的密码和代码。 公众对密码学重要性的认识正在增长，需要了解所涉及的问题。 密码学研究为学生提供了传统的数学技能和概念的有趣背景。 涵盖的数学主题包括珀切斯，概率，功能，质数，小数，倒置和模块化算术。主要产品是一本中学生书籍，并附有随附的教师材料。 正在开发一个支持本书中活动的网站。 还开发了3年级，4和5年级的缩写模块，以及调整在非正式教育环境（例如博物馆和课后课程）中使用材料的讲师指南。 该模块的开发涉及来自不同学校社区的经验丰富的课堂教师和非正式教育计划的讲师进行试验和现场测试。 评估包括数学家和教育者的审查，以及对学生对所研究主题的理解水平的调查。